Related papers: Appell Transformation and Canonical Transforms
The quaternion Fourier transform (QFT), a generalization of the classical 2D Fourier transform, plays an increasingly active role in particular signal and colour image processing. There tends to be an inordinate degree of interest placed on…
This is a mini-review of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered.
The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the…
In this article, we discuss the propagation of scalar fields in conformally transformed spacetimes with either minimal or conformal coupling. The conformally coupled equation of motion is transformed into a one-dimensional…
We study heat radiation and heat transfer for pointlike particles in a system of other objects. Starting from exact many-body expressions found from scattering theory and fluctuational electrodynamics, we find that transfer and radiation…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
The kinetic equation of nonlocal and non-instantaneous character unifies the achievements of the transport in dense quantum gases with the Landau theory of quasiclassical transport in Fermi systems. Large cancellations in the off-shell…
We calculate the radiative heat transfer between two identical metallic one-dimensional lamellar gratings. To this aim we present and exploit a modification to the widely-used Fourier modal method, known as adaptive spatial resolution,…
In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative…
We define hyperbolic fractional-order Fourier transformations by replacing the circular trigonometric functions in the integral expressions of conventional fractional-order Fourier transformations with hyperbolic trigonometric functions. We…
The so-called Weyl transform is a linear map from a commutative algebra of functions to a noncommutative algebra of linear operators, characterized by an action on Cartesian coordinate functions of the form $(x, y) \mapsto (X, Y)$ such that…
Heat can generally transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively.…
This paper is devoted to a prediction of new effect - the occurrence of a heat flow perpendicular both to temperature gradient and magnetic field in molecular dielectric where rotary degrees of freedom of molecules are defrozen. The method…
We derive the asymptotic expansion of the heat kernel for a Laplace operator acting on deformed spheres. We calculate the coefficients of the heat kernel expansion on two- and three-dimensional deformed spheres as functions of deformation…
This tutorial is designed to clarify a few misconceptions in the field of ultrafast optics. (1) Analytic signal that underlies the complex-conjugate decomposition of the field is discussed, as well as the misunderstanding between…
In this note we give an explicit integral representation and an expanssion for the heat kernel $ H_n(t;x,y)$ associated to Fubini-Study Laplacians on quaternionic projective spaces $\mathbb{P}^n(\mathbb H)$, $n \geq 1$. This was possible by…
In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if $\phi$ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition…
Modified Laplace transformation method is applied to N component $\phi^4$ theory and the finite temperature problem in the massless limit is re-examined in the large N limit. We perform perturbation expansion of the dressed thermal mass in…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
This paper is about quantum heat defined as the change in energy of a bath during a process. The presentation takes into account recent developments in classical strong-coupling thermodynamics, and addresses a version of quantum heat which…